How should be change ROOT LOCUS asymmetric?

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x y
x y 2012-11-25
Task is find stabil interval. (root locus)
Code:
num=[1 0 0 0]
den=[1 0 5 10 1.5]
Hs=tf(num,den)
rlocus(Hs)
Result:
num =
1 0 0 0
den =
Columns 1 through 3
1.0000 0 5.0000
Columns 4 through 5
10.0000 1.5000
Transfer function:
s^3
------------------------
s^4 + 5 s^2 + 10 s + 1.5
Plot is asymmetric: http://i.imgur.com/v8dQD.png
Who can me help to solve symetrical plot?
  1 个评论
Azzi Abdelmalek
Azzi Abdelmalek 2012-11-26
编辑：Azzi Abdelmalek 2012-11-26
xy, you've added a comment, then don't use answer (use comment).
What do you want exactly to do? Your question and your comment are not coherents

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采纳的回答

Azzi Abdelmalek
Azzi Abdelmalek 2012-11-25
k=-1000:0.1:1000;
rlocus(Hs,k)

更多回答（2 个）

Jonathan Epperl
Jonathan Epperl 2012-11-25
That's interesting, that harmless looking transfer function really seems to be problematic for Matlab.
You have already noted that the root locus your are getting is certainly wrong -- it is not symmetric wrt the real axis, and also the real axis left of the pole at -1.3 has to lie on the root locus entirely.
Two solutions I can offer:
  • As Azzi has suggested, supply a vector of gain values with higher resolution, I suggest
rlocus(Hs, linspace(0,40,5e3));
  • Instead of drawing the root locus and eyeballing it, do some math to find the imaginary-axis crossings. The Routh-Array and Hurwitz Criteria are favorites here.
x y
x y 2012-11-26
Thi is not same ,but in this task is good,is symethric:
s^3
------------------------
s^4 + 5 s^2 + 10 s + 0.5
s^4 + K s^3 + 5 s^2 + 10 s + 0,5 = 0
omega^4 - K j omega^3 - 5 omega^2 + 10 j omega + 0,5 = 0
omega ^4 - 5 omega^2 + 0,5 = 0
- K j omega^3 + 10 j omega = 0 => k = 10 / omega^2
>> omega=roots([1 0 -5 0 0.5]);
>> k=10./omega.^2
k =
2.041684766872804e+000
2.041684766872800e+000
9.795831523312707e+001
9.795831523312721e+001
>> r1=rlocus(g,k(1))
r1 =
8.049116928532385e-016 +2.213123530591180e+000i
8.049116928532385e-016 -2.213123530591180e+000i
-1.990396370317212e+000
-5.128839655559203e-002
>> r2=rlocus(g,k(3))
r2 =
-9.790828968598125e+001
2.359223927328458e-016 +3.195062414783789e-001i
2.359223927328458e-016 -3.195062414783789e-001i
-5.002554714585826e-002
but i dont know how to get this:
s^4 + K s^3 + 5 s^2 + 10 s + 0,5 = 0
* omega^4 - K j omega^3 - 5 omega^2 + 10 j omega + 0,5 = 0*
* omega ^4 - 5 omega^2 + 0,5 = 0
- K j omega^3 + 10 j omega = 0 => k = 10 / omega^2 *

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